We show how a processor with native extended floating point precision could be incorporated in algebraic subroutines in convex optimisation, namely in indirect matrix inversion methods like Conjugate Gradient, which are used in Interior Point Methods in the case of very large problem sizes. Also, an estimate is provided of the expected acceleration of the time to solution for a hardware running natively on extended precision. Specifically, when using indirect matrix inversion methods like Conjugate Gradient, which have lower complexity than direct methods and are therefore used in very large problems, we see that increasing the internal working precision reduces the time to solution by a factor that increases with the system size.